What is the integral of 1/(sqrt(2x-3)) ?

The integral of 1/(sqrt(2x-3)) is sqrt(2x-3)+C

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integral of 1/(sqrt(2x-3))

\int \frac{1}{2 x - 3} d x

2 x - 3 + C

Solution steps

\int \frac{1}{2 x - 3} d x

Apply u-substitution

: \int 1 d u

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = 2 x - 3

= 1 \cdot 2 x - 3

Simplify

= 2 x - 3

Add a constant to the solution

= 2 x - 3 + C

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What is the integral of 1/(sqrt(2x-3)) ?
The integral of 1/(sqrt(2x-3)) is sqrt(2x-3)+C